Abstract The Hubbard model has been studied for a long time as a simplified model for electron correlation problems such as the metal-insulator transition, itinerant magnetism, and so on. Moreover, the discovery of high 7;, superconductors has again raised an important question about the strong correlation problem near the metal-insulator transition, including low-dimensional quantum fluctuations (Anderson 1987). In recent works, we have precisely studied various thermodynamic properties of the one-dimensional Hubbard model (Kawakami et al. 1989; Usuki et al. 1989) and clarified the underlying physics near the Mott insulator in terms of the dressed particles of the Bethe ansatz method (Kawakami and Okiji 1989a, b). In this brief report, we present the exact calculation for the dressed particles in the Hubbard chain near the Mott insulator.Abstract The Hubbard model has been studied for a long time as a simplified model for electron correlation problems such as the metal-insulator transition, itinerant magnetism, and so on. Moreover, the discovery of high 7;, superconductors has again raised an important question about the strong correlation problem near the metal-insulator transition, including low-dimensional quantum fluctuations (Anderson 1987). In recent works, we have precisely studied various thermodynamic properties of the one-dimensional Hubbard model (Kawakami et al. 1989; Usuki et al. 1989) and clarified the underlying physics near the Mott insulator in terms of the dressed particles of the Bethe ansatz method (Kawakami and Okiji 1989a, b). In this brief report, we present the exact calculation for the dressed particles in the Hubbard chain near the Mott insulator.

Mar 21, 19910 citations

Simulations of the Hubbard model

J. E. Hirsch

Journal of Statistical PhysicsJun 1, 198615 citations

Mean-field study of superconductivity in the t − J square lattice model with three-site hopping

Ke Yang, Qianqian Chen, Lei Qiao +1 more

It remains an open question whether the two-dimensional single-band pure Hubbard model and its related pure $t\text{\ensuremath{-}}J$ model truly capture the superconducting order in cuprates. Recent numerical studies on this issue have raised a notable disparity in superconducting order between the pure Hubbard model and the pure $t\text{\ensuremath{-}}J$ model. Inspired by these works, we investigate the role of the three-site hopping term in $d$ -wave superconductivity, such a term is usually neglected in the effective Hamiltonian of the Hubbard model, although its amplitude is of the same order as the superexchange coupling $J$ in the $t\text{\ensuremath{-}}J$ model. Our slave-boson mean-field solution demonstrates the suppression of $d$ -wave superconducting order by incorporating the three-site hopping term, consistent with numerical observations by the density-matrix renormalization group. This suppression could be understood as a result of competition between superexchange interaction and three-site hopping, the former favors $d$ -wave pairing while the latter favors $s$ -wave pairing. We also discussed its role in quasiparticle dispersion and boson-condensation temperature. Our findings may offer an alternative understanding of the recent numerical contrasting findings in the strong-coupling regime: the absent or weak superconductivity in the pure Hubbard model, while the robust superconductivity in the $t\text{\ensuremath{-}}J$ model without including the three-site hopping term.It remains an open question whether the two-dimensional single-band pure Hubbard model and its related pure $t\text{\ensuremath{-}}J$ model truly capture the superconducting order in cuprates. Recent numerical studies on this issue have raised a notable disparity in superconducting order between the pure Hubbard model and the pure $t\text{\ensuremath{-}}J$ model. Inspired by these works, we investigate the role of the three-site hopping term in $d$-wave superconductivity, such a term is usually neglected in the effective Hamiltonian of the Hubbard model, although its amplitude is of the same order as the superexchange coupling $J$ in the $t\text{\ensuremath{-}}J$ model. Our slave-boson mean-field solution demonstrates the suppression of $d$-wave superconducting order by incorporating the three-site hopping term, consistent with numerical observations by the density-matrix renormalization group. This suppression could be understood as a result of competition between superexchange interaction and three-site hopping, the former favors $d$-wave pairing while the latter favors $s$-wave pairing. We also discussed its role in quasiparticle dispersion and boson-condensation temperature. Our findings may offer an alternative understanding of the recent numerical contrasting findings in the strong-coupling regime: the absent or weak superconductivity in the pure Hubbard model, while the robust superconductivity in the $t\text{\ensuremath{-}}J$ model without including the three-site hopping term.

arXiv:2406.08780Physical review. B./Physical review. BAug 15, 20242 citations

Two results on the Hubbard model

Gang Su

Physics Letters ASep 1, 19962 citations

Intertwined States at Finite Temperatures in the Hubbard Model

Edwin W. Huang, Wen O. Wang, Jixun K. Ding +5 more

Significant advances in numerical techniques have enabled recent breakthroughs in the study of various properties of the Hubbard model - a seemingly simple, yet complex model of correlated electrons that has been a focus of study for more than half a century. In particular, it captures the essence of strong correlations, and is believed to possess various emergent, low energy states and collective excitations characteristic of cuprate high-temperature superconducting materials. While a thorough review of all activity is not possible here, we have focused the discussion on our recent work using unbiased, numerically exact, ``brute force", finite temperature quantum Monte Carlo methods. Our various studies reveal a rich variety of quantum liquid crystal phases, and complementary transport properties, which answer some questions, but certainly raise others concerning ``strange metal" behavior and the ultimate fate of quasiparticles in the Hubbard model.Significant advances in numerical techniques have enabled recent breakthroughs in the study of various properties of the Hubbard model - a seemingly simple, yet complex model of correlated electrons that has been a focus of study for more than half a century. In particular, it captures the essence of strong correlations, and is believed to possess various emergent, low energy states and collective excitations characteristic of cuprate high-temperature superconducting materials. While a thorough review of all activity is not possible here, we have focused the discussion on our recent work using unbiased, numerically exact, ``brute force", finite temperature quantum Monte Carlo methods. Our various studies reveal a rich variety of quantum liquid crystal phases, and complementary transport properties, which answer some questions, but certainly raise others concerning ``strange metal" behavior and the ultimate fate of quasiparticles in the Hubbard model.

arXiv:2106.09704Journal of the Physical Society of JapanSep 3, 202110 citations

d

-wave superconductivity, such a term is usually neglected in the effective Hamiltonian of the Hubbard model, although its amplitude is of the same order as the superexchange coupling

J

in the $t\text{\ensuremath{-}}J$ model. Our slave-boson mean-field solution demonstrates the suppression of

d

-wave superconducting order by incorporating the three-site hopping term, consistent with numerical observations by the density-matrix renormalization group. This suppression could be understood as a result of competition between superexchange interaction and three-site hopping, the former favors

d

-wave pairing while the latter favors

s

-wave pairing. We also discussed its role in quasiparticle dispersion and boson-condensation temperature. Our findings may offer an alternative understanding of the recent numerical contrasting findings in the strong-coupling regime: the absent or weak superconductivity in the pure Hubbard model, while the robust superconductivity in the $t\text{\ensuremath{-}}J$ model without including the three-site hopping term.